• Hidalgo, Ruben A.
  • Received : 2010.12.01
  • Published : 2012.03.31


In 1995 it was proved by Gonz$\acute{a}$lez-Diez that the cyclic group generated by a p-gonal automorphism of a closed Riemann surface of genus at least two is unique up to conjugation in the full group of conformal automorphisms. Later, in 2008, Gromadzki provided a different and shorter proof of the same fact using the Castelnuovo-Severi theorem. In this paper we provide another proof which is shorter and is just a simple use of Sylow's theorem together with the Castelnuovo-Severi theorem. This method permits to obtain that the cyclic group generated by a conformal automorphism of order p of a handlebody with a Kleinian structure and quotient the three-ball is unique up to conjugation in the full group of conformal automorphisms.


Riemann surfaces;conformal automorphisms;fixed points


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  1. On automorphisms groups of cyclic p-gonal Riemann surfaces vol.57, 2013,
  2. On the uniqueness of (p, h)-gonal automorphisms of Riemann surfaces vol.98, pp.6, 2012,